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Bulletin of the London Mathematical Society 1994 26(2):127-131; doi:10.1112/blms/26.2.127
© 1994 by London Mathematical Society
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© London Mathematical Society

The Strength of a Fabric

C. R. J. Clapham

Chancellor College, University of Malawi P.O. Box 280, Zomba, Malawi

Received 23 June 1992. Revision received 23 December 1992.

Consider fabrics in which every warp (and weft) strand passes over and under at least k weft (warp) strands. There is a 4k by 4k fabric of this kind that does not hang together. We prove that any n by n fabric of this kind, where n < 4k, does hang together. Moreover, we introduce a measure of how well a fabric hangs together, by defining the strength of a fabric, and two theorems are proved that extend the preceding results.


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